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Solving Optimization Tasks by ACO Algorithms
Habrnál, Matěj ; Samek, Jan (referee) ; Zbořil, František (advisor)
The presented thesis puts its main focus on the basic optimization algorithms ACO (Ant Colony Optimization) and their development and seeks the inspiration in the ants live. The aim is to demonstrate the activity of these algorithms on optimization problems - the traveling salesman problem and the finding food sources problem and optimal routes between an anthill and food. The thesis also describes experiments that try to determine the influence of adjustable parameters of ant algorithms. First, ACO algorithms theory is described followed then by the application of these algorithms on both selected optimization problems. The conclusion sums up experiments analysis with established applications and evaluating prospective results.
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Travelling Salesman Problem
Kolář, Adam ; Rozman, Jaroslav (referee) ; Zbořil, František (advisor)
The aim of this bachelor's thesis is to design a testing environment for the traveling salesman problem and compare the effectiveness of different approaches to the solution. The first part discussed the possibility of genetic algorithms, depending on the setting of a crossover, mutations and population size. In the second part, there is the same problem using two types of neural networks. The representative of the self-learning net was chosen Kohonen neural network. Hopfield neural network represents a method of minimizing the energy function with fixed coefficients. At both neural networks, there were described possible advantages and disadvantages. In the end, all the findings were interpreted in a global context.
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The global optimalization methods
Dudová, Aneta ; Kozumplík, Jiří (referee) ; Mézl, Martin (advisor)
This bachelor work is dedicated to advanced methods of global optimization, and especially problem traveling salesman. It focuses on the description of the problem and its various options, including graph theory, heuristic algorithms, evolutionary algorithms, in which mainly genetic algorithms and optimization by ant colonies. In conclusion, the implementation of these methods and performed testing on different data sets of algorithms that approximately solve the traveling salesman problem.
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On-line games and Graph Theory
Hillebrandová, Eliška ; Jančařík, Antonín (advisor) ; Pilous, Derek (referee)
Graph theory is a full-featured topic of modern mathematics as mathematical analysis or algebra. However, it is closest to geometry, as evidenced by its original geometric of position. In this work I focus on familiarizing readers with this theory, including its rich history. Unlike other branches of mathematics, graph theory was created as a solution to various games and puzzles. That's why I represent the most significant graph theory games, have found their place in the modern world through on-line games for mobile devices and computers. The games are: Galaxy, Icosien and Wired. Galaxy is a game that focuses on searching for Eulerian path in a graph. In Icosien, we try to find a Hamilton circle of the graph, and the Wired game needs to break the graph crossed, which is plannar graph. The first chapter deals with the introduction of these concepts needed to understand the given issue. The second chapter focuses on the origin and development of problems that led to the theory of graphs as the discipline itself. The final chapter contains the structure of on-line games, their rules and examples with solutions. In GeoGebra, I illustrate a solution of these examples in five different difficulties. The output of the thesis is not only the compilation of theoretical knowledge and historical set-up, but...
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Chessboard problems in combinatorics
Chybová, Lucie ; Slavík, Antonín (advisor) ; Šmíd, Dalibor (referee)
This master thesis discusses various mathematical problems related to the placement of chess pieces. Solutions to the problems are mostly elementary (yet sometimes quite inventive), in some cases rely on basic knowledge of graph theory. We successively focus on different chess pieces and their tours on rectangular boards, and then examine the "independence" and "domination" of chess pieces on square boards. The text is complemented with numerous pictures illustrating particular solutions to given problems.
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The global optimalization methods
Dudová, Aneta ; Kozumplík, Jiří (referee) ; Mézl, Martin (advisor)
This bachelor work is dedicated to advanced methods of global optimization, and especially problem traveling salesman. It focuses on the description of the problem and its various options, including graph theory, heuristic algorithms, evolutionary algorithms, in which mainly genetic algorithms and optimization by ant colonies. In conclusion, the implementation of these methods and performed testing on different data sets of algorithms that approximately solve the traveling salesman problem.
|
|
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Travelling Salesman Problem
Kolář, Adam ; Rozman, Jaroslav (referee) ; Zbořil, František (advisor)
The aim of this bachelor's thesis is to design a testing environment for the traveling salesman problem and compare the effectiveness of different approaches to the solution. The first part discussed the possibility of genetic algorithms, depending on the setting of a crossover, mutations and population size. In the second part, there is the same problem using two types of neural networks. The representative of the self-learning net was chosen Kohonen neural network. Hopfield neural network represents a method of minimizing the energy function with fixed coefficients. At both neural networks, there were described possible advantages and disadvantages. In the end, all the findings were interpreted in a global context.
|
|
|
Solving Optimization Tasks by ACO Algorithms
Habrnál, Matěj ; Samek, Jan (referee) ; Zbořil, František (advisor)
The presented thesis puts its main focus on the basic optimization algorithms ACO (Ant Colony Optimization) and their development and seeks the inspiration in the ants live. The aim is to demonstrate the activity of these algorithms on optimization problems - the traveling salesman problem and the finding food sources problem and optimal routes between an anthill and food. The thesis also describes experiments that try to determine the influence of adjustable parameters of ant algorithms. First, ACO algorithms theory is described followed then by the application of these algorithms on both selected optimization problems. The conclusion sums up experiments analysis with established applications and evaluating prospective results.
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